Stabilisation de certains systèmes d’évolution non linéaires
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Date
2023
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Abstract
This thesis investigates the qualitative aspects of solutions for a specifc class of heat equations with logarithmic nonlinearity governed by the p(x)-Laplacian. The focus is on exploring stability, existence of global solutions, and blow-up phenomena in their behavior. The variable exponent p(x) introduces spatial dependency, while the temporal evolution of the system is captured by the heat equation. These equations are both mathematically difcult and fascinating to study due to the presence of such variable exponents and the logarithmic nonlinearity in them. The main goals of this study are to investigate the stability characteristics of solutions, identify the prerequisites for their global existence, and examine the occurrence of blow-up in fnite time.